Question: Solve for $y$, $ \dfrac{6}{5y + 10} = \dfrac{3y - 6}{3y + 6} - \dfrac{1}{y + 2} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5y + 10$ $3y + 6$ and $y + 2$ The common denominator is $15y + 30$ To get $15y + 30$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{6}{5y + 10} \times \dfrac{3}{3} = \dfrac{18}{15y + 30} $ To get $15y + 30$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{3y - 6}{3y + 6} \times \dfrac{5}{5} = \dfrac{15y - 30}{15y + 30} $ To get $15y + 30$ in the denominator of the third term, multiply it by $\frac{15}{15}$ $ -\dfrac{1}{y + 2} \times \dfrac{15}{15} = -\dfrac{15}{15y + 30} $ This give us: $ \dfrac{18}{15y + 30} = \dfrac{15y - 30}{15y + 30} - \dfrac{15}{15y + 30} $ If we multiply both sides of the equation by $15y + 30$ , we get: $ 18 = 15y - 30 - 15$ $ 18 = 15y - 45$ $ 63 = 15y $ $ y = \dfrac{21}{5}$